Question

. A web-based algorithm classifies emails as spams or no-spam at a success rate of 70% of detecting a spam. A. Find a 95% confidence interval for the number of spam emails expected within a sample of 100 emails. B. Find a 95% confidence interval for the accuracy (standard deviation) of the detected number of spams within the 100 emails. C. Determine the probability that at least 85 emails out of 100 emails are spams. D. If for the 100 emails above, there was indeed actually 85 spam emails, test the claim that the same algorithm can still detect at least 85 emails with a 95% confidence.

Answer 1

the probability that the success rate of detecting spam is p = 0.70

A) For sample of n= 100

mean = np = 100*0.70 =70

standard deviation =

95% confidence interval for the expected number of spam emails is

for 95% confidence

rounding off to a nearest integer

B)

c) This probability can be calculated using the binomial distribution

The probability that at least 85 emails out of 100 emails are spams =